This invention relates to computer-assisted design (CAD) systems and specifically relates to a system and method for generating two-dimensional and three-dimensional surface meshes and for unwrapping and flattening three-dimensional surfaces into two-dimensional pattern shapes. The present invention has specific application to the footwear, furniture, automotive, aerospace and medical industries.
In U.S. Pat. No. 5,107,444 issued Apr. 21, 1992 to Chien Tai Wu for a METHOD AND APPARATUS FOR FLATTENING THREE-DIMENSIONAL SURFACES, the disclosure of which is hereby incorporated herein by reference, a unique solution was provided to the task of converting in a computer-assisted design system a three-dimensional image into a two-dimensional flat pattern that is a true representation of the three-dimensional surface of the object. For three-dimensional surfaces that possess regions having substantial amounts of Gaussian curvature, such as spheroidal surfaces and saddles, the flat pattern solution is not even developable in all regions. The Wu invention provided an optimum numerical solution that provided minimum deviation from the true solution to the flattening problem in regions of substantial amounts of Gaussian curvature. This is accomplished in a computer-assisted design system by generating a three-dimensional mesh conforming to the topology of the three-dimensional surface and including lines intersecting at nodal points to define polygonal elements between the nodal points. The polygonal elements were mapped to a location in a two-dimensional flat plane where the polygonal elements share at least one side with other polygonal elements previously mapped to the flat plane. The length of the shared side is distorted to conform to the length of the shared side of the other polygonal element. The distance between corresponding nodal points in the flat plane and on the three-dimensional surface are compared in order to determine the amount of distortion and are adjusted in response to the results of the comparison. This global adjustment is recursively carried out every time a complete row of elements is added to the developing pattern and when the pattern is complete.
Because the method of the Wu patent cannot be guaranteed to provide a true solution in regions of high Gaussian curvature, it additionally provides a function that compares the length of the sides of the polygonal elements in the three-dimensional image with the same sides in the two-dimensional image. If a side is shorter in the two-dimensional image, then localized "compression" exists and, if the side is longer, localized tension exists. Such determined compression and tension are displayed for each such polygonal element side by the use of a color bar displaying a range of hues which are displayed on the mesh element of the two-dimensional pattern shape. The Wu patent further provides tools by which the user may apply his or her creativity and experience to make modifications to the pattern piece. The modifications, or cuts, are mapped back to the three-dimensional surface, which is then reflattened in order to determine the effect of the user-initiated modifications on the tension and compression stress distribution.
In practical applications of three-dimensional CAD systems, it is conventional to model the surface of complex objects, such as automobile seats and medical prothesis implant covers by tiling many surfaces together to define the form of the object. For example, an automotive seat bottom, seat back or seat head rest is each typically defined by up to 10 or more different mathematical surfaces. Each surface combined in this manner has its own parameter space and mathematical definition. As a result, the boundaries of the mathematical surfaces do not necessarily define the particular surface region of a three-dimensional object for the purposes of unwrapping and flattening the three-dimensional object into a two-dimensional pattern shape. Where one or more of the surfaces that are tiled together to form the surface region of the three-dimensional object includes multiple nondevelopable adjacent surfaces, the ability to find an optimum solution is further complicated.